EVALUATING THE ACCURACY OF A GRAVIMETRIC SURVEY 145 



Within the range x^—Xi = a, we consider that the true values of gravity 

 vary in a hnear manner. 

 Hence we have 



For a certain point x, within the range {x■^^, x^ the following relationship 

 will hold 



g (-^) -g {^) = £0 = 0^1 + — ~ {x-Xi) 



I 1 -^ "^^ 



-0 



Assuming that a;^ = and bearing in mind that the observational errors 

 Gi and (72 are independent and random, after squaring we obtain 



eQ^ = -^{a^-2ax+2x^). 

 The integral mean of this value within the range < ^ < a has the form : 



^Qm 



Ih 



Integrating, we obtain 



p2 _ _ ^2 



Thus, Eq^ depends only on the mean square error in the values of 

 gravity at the observation points. 



2. The derivation of the relationship ^q^ = Sq^ (a, a, p). 



As the points x^, x^, x^ let there be true values of gravity g-^, g-g, ^3 and 

 the observed values ^1, ^2? g^ ^^\h errors cTj, a^^ a^ (Fig. 3). Within the ran- 

 ges x^—X2 = ATg— % = a, the change in the force of gravity will be consi- 

 dered linear. Let us select in the range {x^, x^ two such points x^ and % 

 for which the difference in the interpolated values of gravity g^ and g^ is 

 equal to the cross-section of the isoanomahes p, i.e. g^—g^ = />• 



Assuming x^—x^ = d^a,\fe find the expression 



^0 = ig5-gi)-ig5-g4)- 



Applied geophysics 10 



